Republican presidential hopeful Herman Cain faced a new set of political challenges Monday after graphic allegations by a Chicago woman raised questions among GOP operatives and activists about the candidate’s ability to survive the growing scandal.

After eight days of accusations and denials of alleged sexual harassment by Cain, the specific and explicit nature of the new allegations could threaten his position among a core group of supporters who have stood by him, or at least stayed silent.

“This is the first time that the allegations have been about physical rather than verbal harassment. These are much more serious charges that require Cain to provide a more specific explanation than a blanket denial,” said Daniel Schnur, who advised Sen. John McCain’s 2000 presidential campaign but is uncommitted in the 2012 contest.

Mississippi Gov. Haley Barbour told the conservative magazine National Review on Monday: “If there is any substance to the claims, if the American people believe that somebody abused women, they are not going to elect him or her president. If this were taken as being true, and people believe it’s true, then I don’t think that can be overcome.”

The initial allegations against Cain — dating to the 1990s, when he was chief executive of the National Restaurant Association — were general and unspecific, and Cain denied them.

Sharon Bialek changed that Monday with a nationally televised news conference in which she accused Cain of groping her and trying to force her into a sexual act.

Cain’s campaign issued another denial but did not respond directly to Bialek’s claims: “All allegations of harassment against Mr. Cain are completely false,” said J.D. Gordon, a Cain spokesman. “Mr. Cain has never harassed anyone.” Gordon characterized Bialek’s charges as “bogus attacks.”

Cain himself went on ABC’s ‘Jimmy Kimmel Live’ Monday night to vow he is “taking this [accusation] head on.” “There’s not an ounce of truth in all of these allegations,” he declared, but they seem to be altering the political calculus for the candidate.

“This changes the dynamic of the situation,” said Craig Robinson, a longtime Republican operative in Iowa who runs a political blog there. “Last week, the defenders of Herman were saying these are all anonymous people. Now we have a woman who has come forward in pretty plain language about what went on. He can’t just blame the media on this one.”

As the news of sexual harassment charges filed against Cain in the 1990s emerged last week, many conservatives blasted the accusations as anonymous sniping against a leading Republican contender and blamed the “liberal media.”

But Bialek’s comments will almost certainly force the former Godfather’s Pizza chief executive to offer his own version of his interactions with the woman, Republicans say. And the continuing focus on alleged sexual harassment in his past could push conservative voters who galvanized behind Cain to defect. That could significantly reorder the already topsy-turvy GOP race that has been defined by sudden surges by different candidates in opinion polls, followed by equally sudden collapses or setbacks.

Although the earlier allegations did not seem to faze some of Cain’s supporters, Bialek’s accusations seem to raise doubts among some.

Robert Haugen, who runs an investment research firm in Colorado and has donated $1,000 to Cain’s campaign this year, said in an interview after Monday’s news conference that the sexual harassment allegations make him “a little less supportive” of Cain.

“I suspect he’s being dishonest, and I don’t want that in a president,” Haugen said. “The dishonesty bothers me more than the sexual aggressiveness.”

But other Cain backers are sticking with the candidate.

“I don’t trust any of it,” said Fred Backer Jr., 71, a retired correctional officer in Mount Morris, N.Y., who has donated more than $1,000 to Cain’s campaign. “The man’s been in business for 40-some years without a blemish. He’s had to work with people both male and female all that time. It’s so out of character for him, it’s unbelievable.”

Backer, who watched Bialek’s news conference, added, “He’s my man. “I’ve been giving him $150 a month out of my Social Security every month since May, and I’m going to keep doing that until he’s not running.”

And antiestablishment conservative activists, who defended Cain last week, were skeptical of Bialek’s allegations.

“She was not employed by the restaurant association when this happened. There are no witnesses. She told nobody at the time that it happened, and he is denying it,” conservative talk radio host Rush Limbaugh said on his show Monday.

Bialek’s news conference came just as the furor was dying down over the news, first reported by Politico, that the National Restaurant Association had settled a sexual harassment claim against Cain in the 1990s when he led the association. A Washington Post-ABC News poll released Friday showed that Cain has survived the controversy politically; the survey showed him effectively tied for the lead in the GOP nominating race with former Massachusetts governor Mitt Romney.

But Bialek’s comments are likely to cause even more criticism from more establishment figures in the party who were already wary of Cain, whom many Republicans view as a weak candidate to face President Obama next year.

What’s not clear is whether many Republican voters will abandon Cain. His strength in the polls over the past month has remained despite not only the sexual harassment charges but also rivals’ attacks of his “9-9-9” tax plan. An NBC News-Wall Street Journal poll conducted before Bialek’s news conference found that a majority of Republicans were not concerned about the sexual harassment allegations.

Much of Cain’s support comes from the antiestablishment tea party wing of the GOP, which has been resistant to Romney but abandoned Bachmann and Texas Gov. Rick Perry after galvanizing behind both earlier in the race. If the sexual harassment allegations result in a significant loss of support for Cain, that could reshape the Republican race, perhaps offering a second chance for Bachmann or Perry or elevating another candidate, such as former House speaker Newt Gingrich (Ga.).

Republicans say what happens to Cain’s campaign will largely rest on the candidate himself and whether Republicans trust his denials of the multiple allegations of improper sexual behavior.

“The thing is how much is true,” said Steve Scheffler, a longtime conservative activist in Iowa. “We have to see the real facts.”